Donald W. Loveland, Richard E. Hodel, and S. G. Sterrett: Three Views of Logic: Mathematics, Philosophy and Computer Science

This is a textbook based on an interdisciplinary (advanced undergraduate level) course that was originally taught by the three authors at Duke. It is intended for many different disciplines. Even though it covers mathematical and philosophical topics, it occasionally still feels like a textbook whose origins lie more in computer science than in the other disciplines. This isn’t even surprising, for an interdisciplinary focus on logic easily draws one towards computer science and artificial intelligence. In three parts, each written by one of the authors, a three-chapter overview is given of the topics of proof-theory, computability-theory and philosophical logic. Yet, rather than a juxtaposition of logical, mathematical, computational, and philosophical subjects, this textbook isn’t merely intended as an illustration of how logic is relevant for many different disciplines, but forms the basis for a different kind of introduction to logic. This reviewer surely applauds the intent to teach logic to philosophers more like we would teach it to computer scientists—with an emphasis on what it allows us to achieve, but also to teach it to computer scientists more like we would (or ought to) teach it to philosophers—with more attention to the diversity in logic than to the dominant background role of classical logic. While Part 1 is concerned with proof-theory, with chapters on classical propositional logic, first-order logic, and Prolog, it also double-tasks as an introduction to formal logic. Thus, chapter 1 reviews the language and semantics of propositional logic, and even goes on to prove two basic meta-theoretical results by